Field of the Invention
The invention relates to a method for channel equalization of received data that is being transmitted via a transmission channel, in which setting coefficients for filters and equalizers are determined with little computation effort and at a high computation rate.
One serious problem in communications systems is multipath signal propagation. FIG. 1 is provided to explain the problems of multipath propagation. There are generally a number of possible signal propagation paths between a base station or transmitter S and a mobile station acting as a receiver E. Reflection and scatter of signal waves on buildings, mountains, trees, and other obstructions mean that the received field strength is composed of a number of signal components which in general have different intensities and different delays.
The transmission channel between the transmitter S and the receiver E can be modeled, in order to take account of multipath propagation, as a transmission filter channel H with channel coefficients hk, as is illustrated in FIG. 2. The transmitter S emits transmitted data or transmitted symbols Sk, via the transmission channel H, to a model adder that accounts for the superimposition of a noise signal on the transmitted signals Sk that have been filtered by hk. The transmitted data symbols Sk may have a number of states, for example, eight states that are coded using 3 bits. The noise signal hk represents additive, white Gaussian noise with a variance σ2n, and is not correlated with the transmitted signal symbols Sk.
The transmitted signals Sk that have been filtered by the transmission channel H and that have had noise superimposed on them, are received by the receiver as a received signal Xk, for which:                               X          k                =                                            ∑                              i                =                0                            L                        ⁢                                                   ⁢                                          h                i                            ⁢                              S                                  k                  -                  i                                                              +                      n            k                                              (        1        )            where L is the order of the modeled transmission channel filter H. As can be seen from equation 1, there is an intersymbol interference (ISI) problem with the received data, since Xk is dependent not only on Sk, but also on Sk−1 . . . , Sk−L. Unless it is compensated for, the intersymbol interference (ISI) leads to high bit error rates. An equalizer is used within the receiver E in order to compensate for the intersymbol interference. This is normally a linear equalizer, decision feedback equalizer (DFE), or a so-called Viterbi equalizer.
FIG. 3 schematically shows a conventionally designed prior art receiver E. The received signal Xk passes, via an internal line, to an input filter P with filter coefficients Pk. The input signal Yk, which has been filtered by the input filter P, is supplied to an equalizer EQ, and is equalized. The equalized signal is emitted from the equalizer EQ, via an internal line, to a data processing circuit DP for internal data processing. The input filter P is an FIR filter, and can be described by the following equation:       Y    k    =            ∑              i        =        0            N        ⁢                   ⁢                  p        i            ⁢              x                  k          -          i                    
The filter coefficients Pk are set by a controller C via a control line SL1. The equalizer EQ is likewise set by the internal controller C via a control line SL2. To this end, the controller C receives the received signal x(k) via an internal data line DL, and evaluates it in order to set the filter coefficients Pk and the equalizer coefficients gk.
The order of the input filter P is N, and is governed by the hardware configuration of the input filter P.
The equalizer EQ is, for example, a Viterbi equalizer, which uses the so-called Viterbi algorithm. In a Viterbi equalizer, the number of computational operations required increases exponentially with the number of transmission channel coefficients h. To be more precise, the number of computational operations required in the Viberti algorithm increases in proportion with the data transmission rate and with an exponential term mL+1, where m represents the number of possible data signal states of the symbol S. Since the order of an actual transmission channel L is relatively high and the computation complexity of the Viterbi algorithm is thus very high, Viterbi equalizers are frequently used in such a way that the last channel coefficients are ignored or are cut off, in order to minimize the computation complexity. This reduces the quality of the equalization of the received signal, of course. As an alternative to Viterbi equalizers, prior art receivers E use MMSE-DFE equalizers (MMSE-DFE: minimum mean square error decision feedback equalizer), in particular for xDSL receivers.
FIG. 4 shows the internal design of such an MMSE-DFE equalizer in detail. The MMSE-DFE contains a subtractor that subtracts a feedback filter signal gk, which has been filtered by a feedback filter G, from the received signal y(k), which has been filtered by the input filter P. The subtractor uses an internal line to feed the result of the subtraction to a decision-making device, for example a Schmitt trigger circuit. The feedback filter G is of the same order as the transmission channel, namely L.
The feedback filter G can be described by the following equation:                               q          k                =                              ∑                          i              =              1                        L                    ⁢                                           ⁢                                    g              i                        ⁢                                          s                                  k                  -                  N                  -                  i                                            .                                                          (        3        )            
The input signal Zk to the decision-making device is, accordingly, as follows:       Z    k    =                    ∑                  i          =          0                N            ⁢                           ⁢                        p          i                ⁢                  x                      k            -            i                                -                  ∑                  i          =          1                L            ⁢                           ⁢                        g          i                ⁢                              s                          k              -              N              -              i                                .                    
The filter coefficients Pk, gk are set such that Zk corresponds to the transmitted signal sequence Sk−N, as much as possible. The discrepancy ek is defined as follows:                               e          k                =                                            S                              k                -                N                                      -                          Z              k                                =                                                    ∑                                  i                  =                  0                                L                            ⁢                                                           ⁢                                                g                  i                                ⁢                                  s                                      k                    -                    N                    -                    i                                                                        -                                          ∑                                  i                  =                  0                                N                            ⁢                                                           ⁢                                                p                  i                                ⁢                                  x                                      k                    -                    i                                                  ⁢                                                                   ⁢                                                      (                                                                  g                        0                                            ≡                      1                                        )                                    .                                                                                        (        5        )            
The power of the second moment of the discrepancy signal sequence is minimized in order to calculate the input filter coefficients Pk and the feedback filter coefficients gk from the transmission signal channel impulse response coefficients h0, h1 . . . hL and from the signal-to-noise ratio.
The computation complexity for MMSE-DFE is also considerable, so that it cannot be used for actual data transmission channels whose transmission channel order L is high.
The following documents generally describe the prior art relating to the present invention. The article “Givens Rotation Based Least Squares Lattice and Related Algorithms” by Fuyun Ling, which appeared in IEEE Transactions on Signal Processing, Volume 39, No. 7, 1991, pages 1541-1551, which represents the prior art that is closest to the present invention, describes calculations for coefficients of a least-squares equalizer by forming a triangular matrix. The calculations are carried out by applying a number of successive GIVENS matrix rotations to a data matrix that is filled with received data symbols. The coefficients of the equalizer can be read from the triangular matrix once the GIVENS rotations have been carried out.
The article “Soft-Decision Feedback Equalizer for Continuous Phase Modulated Signals in Wideband Mobile Radio Channels” by Joseph C. S. Cheung and Raymond Steele, which appeared in IEEE Transactions on Communications, Volume 42, No. 2/3/4, 1994, pages 1628-1638, proposes that a decision feedback equalizer (DFE) be combined with a Viterbi algorithm for equalization of CPM (Continuous Phase Modulation) signals.
The article “Adaptive Combined DFE/MLSE Techniques for ISI Channels” by Yonghai Gu and Tho Le-Ngoc, which appeared in IEEE Transactions on Communications, Volume 44, No. 7, 1996, pages 847-857, relates to a decision feedback equalizer which is integrated in a receiver that is designed to carry out a maximum likelihood estimation process on data sequences.